A kinetic theory of classical simple liquids

Abstract

A dynamical equation for simple classical liquids is presented which is obtained by a systematic approximation for the memory function of the conventional, equilibrium-averaged, phase-space correlation function. This "kinetic" equation is non-Markovian and spatially nonlocal. It agrees with the known limiting behavior at high and low frequencies $\omega$ and wave vectors $\overrightarrow{\mathrm{k}}$ even for dense liquids. For intermediate $k$ and $\omega$, our equation represents an explicit interpolation model from which virtually all measurable dynamical properties of the simple one-component fluid can be obtained. This equation can be solved analytically. As an example, the dynamical structure factor $S_{\mathrm{nn}}(k, \omega )$ for liquid argon near its triple point was calculated. Our results are in excellent agreement with both coherent-neutron-scattering experiments (for $k=1-4\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$) and computer-dynamics results (for $k<\mathrm{}1\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$). We want to emphasize that no adjustable parameters are introduced. We believe that this is the first kinetic theory which gives satisfactory results for $S_{\mathrm{nn}}(k, \omega )$ for the full range $k$, $\omega$ for which data are available.